Shunt Resistor Selection for High-Accuracy, Optically Isolated Sigma-Delta Modulator Current-Sensing Solution By Lim Shiun Pin, Technical Marketing Engineer, Isolation Products Division, Broadcom Limited
White Paper
Abstract Broadcom Optically Isolated Sigma-Delta As modern factory automation (including servo motors, Modulator industrial robots, and computer numerical control [CNC] Broadcom offers a wide selection of isolated sigma-delta machines) trends toward higher precision, power, speed, modulators with various small-form, standard surface-mount multi-axis, and multi-direction, the requirement for accurate packages suitable for volume production. Combined with sensing of motor phase current has become ever more superior optical coupling isolation technology, Broadcom demanding. Traditionally, current sensing is performed by a sigma-delta modulators deliver high noise margins and current transformer (CT) or Hall Effect Sensor (HES), but these excellent immunity against isolation-mode transients. Boasting solutions are bulky, expensive, and less accurate over operating a minimum distance through insulation (DTI) of 0.5 mm, these temperatures. A smaller, low-cost solution can be easily sigma-delta modulators provide reliable double protection realized by connecting a shunt resistor directly to the and a high working voltage suitable for fail-safe designs. This sigma-delta modulator. Phase current flows through a shunt proven isolation performance is superior to magnetic or resistor with the resistance value selected such that the capacitive-based isolators, where DTI is only a third of 0.1 mm. maximum current range corresponds to an optimum Additionally, since signals are optically transmitted through the recommended low-input voltage range of the sigma-delta isolation barrier, Broadcom’s sigma-delta modulators are modulator. At this low voltage, power dissipation loss across immune to external magnetic fields and absent of hysteresis the shunt resistor is minimized. effect remanence when the external magnetic field is removed. Figure 1 shows the sigma delta product tree.
Figure 1 Broadcom Isolated Sigma-Delta Modulator Product Tree
Isolator Type Isolated Sigma-Delta Modulator
Input Range ±50 mV ±200 mV
Clock Source, Int. Clk, Int. Clk, Ext. Clk, Ext. Clk, Frequency 10 MHz 10 MHz 5~20 MHz 5~25 MHz
Output Interface CMOS/TTL CMOS/TTL CMOS/TTL LVDS
Working Voltage 1414Vpeak 891Vpeak 1414Vpeak 1414Vpeak 1414Vpeak
Part Number ACPL-C799 ACPL-7970 HCPL-7860 HCPL-7560 ACPL-C797 HCPL-786J ACPL-796J ACPL-798J
Gain Accuracy, 1%, 1%, 1%, 5% max., 1%, 2%, 1%, 1%, 0.3 μV/°C, 2 μV/°C, 2 μV/°C, 2 μV/°C, 1 μV/°C, 2 μV/°C max., 3.5 μV/°C max., 1 μV/°C,
Offset Drift, SNR 77 dB 78 dB 73 dB 53 dB 78 dB 73 dB 80 dB 82 dB
Broadcom - 1 - Shunt Resistor Selection for High-Accuracy, Optically Isolated Sigma-Delta Modulator ACPL-C799 ±50 mV Input Internally Clocked Sigma-Delta Modulator Current-Sensing Solution White Paper
ACPL-C799 ±50 mV Input Internally Clocked Sigma-Delta Modulator The Broadcom ACPL-C799 is the Industry’s first ±50 mV input optically isolated sigma-delta modulator. The new device features a low-differential input range of ±50 mV, allowing designers to reduce power dissipation across a current-sensing shunt resistor in servo drive and motor applications. Figure 2 shows a typical application circuit using the ACPL-C799 in a motor phase current-sensing mode.
Figure 2 Typical Application Circuit Using ACPL-C799 in Motor-Phase Current Sensing Mode
Floating Positive Supply HV+
Gate R1 Isolation Non- Drive Barrier Isolated Circuit 5V/3.3V D1 5.1V V R2 V DD1 DD2 4.3
Motor V IN + MCLK + C2 C1b C1a C3a C3b 100 nF 10 μF 0.1 μF 0.1 μF 10 μF R SENSE V IN MDAT
GND1 GND2
ACPL- C799 GND1 GND2
This latest addition to Broadcom's market-leading optically isolated current-sensing portfolio enables higher efficiency through shunt resistor size reduction while delivering improved performance with unparalleled robustness. Compared to previous generation products with an input range of ±200 mV, the ACPL-C799 enables the use of a smaller shunt resistor with one-quarter the value, thereby eliminating 75% of the shunt resistor's power losses. Despite the reduced input voltage range, the device delivers superb SNR, ENOB, and offset drift performance, enabling high-precision motor control in space-constrained, high-temperature environments. Normally, shunt resistors exhibit a continuous power rating of less than 10W. Figure 3 shows that with a lower input voltage of ±50 mV, this allows ACPL-C799 to sense higher current ranges up to 200A in conjunction with low-cost, easily available shunt resistors.
Figure 3 Shunt Resistor Values and Power Rating Requirement vs. Current-Sensing Range
Resistance Power (mΩ) Shunt Resistor Selection Dissipation (W) 20 40
I 35 + To meet power rating requirements: V |ΔV| 15 – R = 30 1. May need to parallel two or more shunt resistors I to share the power load dissipation. 25 2. Implement heat sink. Resistance Power 10 Dissipation 20 3. Customized shunt resistor with larger form factor.
15
5 10
5 Shunt resistors with power rating ±200 mV <10W are easily available in the ±50 mV market. 0 0 10 30 50 70 90 110 130 150 170 190 Current Sensing Range (A)
Broadcom - 2 - Shunt Resistor Selection for High-Accuracy, Optically Isolated Sigma-Delta Modulator Shunt Resistor Selection Current-Sensing Solution White Paper
Shunt Resistor Selection The current-sensing shunt resistor should have low resistance to minimize power dissipation, low inductance to minimize di/dt-induced voltage spikes that could adversely affect operation, and reasonable tolerance to maintain overall circuit accuracy. Choosing a particular value for the shunt is usually a compromise between minimizing power dissipation and maximizing accuracy. Smaller shunt resistances decrease power dissipation, while larger shunt resistances can improve circuit accuracy by utilizing the full input range of the isolated modulator.
Figure 4 Motor Output Horsepower vs. Motor Phase Current and Supply
110
100 440 Vac
90 380 Vac 80 220 Vac 70 120 Vac 60 50 40
Motor Output Power (hp) 30 20 10 0 0 102030405060708090100
Motor Phase Current (ARMS )
Determining Shunt Resistor Values
The first step in selecting a shunt is to determine how much current the shunt will be sensing. The graph in Figure 4 shows the RMS current in each phase of a three-phase induction motor as a function of average motor output power (in horsepower) and motor drive supply voltage. The maximum value of the shunt is determined by the current being measured and the maximum recommended input voltage of the isolated modulator. The maximum shunt resistance can be calculated by taking the maximum recommended input voltage and dividing it by the peak current that the shunt should see during normal operation.
Example
A motor has a maximum RMS current of 70ARMS and can experience up to 50% overload during normal operation. Using the ACPL-C799 for current sensing, the shunt resistor value is calculated to be 0.5 mΩ. The maximum average power dissipation in the shunt can also be determined by multiplying the shunt resistance by the square of the maximum RMS current, which is about 2.45W. The following list shows the detailed calculations.
ACPL-C799 recommended linear input range: ±50 mV ACPL-C799 recommended full-scale range (FSR): ±80 mV
Maximum RMS current through the motor: 70ARMS Peak current: 100A Overload during normal operating condition: 50%
Broadcom - 3 - Shunt Resistor Selection for High-Accuracy, Optically Isolated Sigma-Delta Modulator Shunt Resistor Selection Current-Sensing Solution White Paper
Determining shunt resistor value:
Calculated shunt resistor value (50 mV/100A)—0.5 mΩ
Shunt resistor power dissipation (70ARMS × 70ARMS × 0.5 mΩ)—2.45W Sigma-delta modulator input during overload condition (100A × 50% × 0.5 mΩ)—±75 mV (within the ACPL-C799 FSR) If the power dissipation in the shunt is too high, the resistance of the shunt can be decreased below the maximum value to decrease power dissipation. The minimum value of the shunt is limited by the precision and accuracy requirements of the design. As the shunt value is reduced, the output voltage across the shunt is also reduced, which means that the offset and noise (both fixed) become a larger percentage of the signal amplitude. The selected value of the shunt should fall somewhere between the minimum and maximum values, depending on the particular requirements of a specific design.
Shunt Resistor Temperature Coefficient Consideration
When sensing currents are large enough to cause significant heating of the shunt, the temperature coefficient (tempco) of the shunt can introduce nonlinearity due to the signal-dependent temperature rise of the shunt. The effect increases as the shunt-to-ambient thermal resistance increases. This effect can be minimized either by reducing the thermal resistance of the shunt or by using a shunt with a lower tempco. Lowering the thermal resistance can be accomplished by repositioning the shunt on the PCB, by using larger PCB traces to carry away more heat, or by using a heat sink.
Two-Terminal vs. Four-Terminal Shunt Resistor
For a two-terminal shunt, as the value of shunt resistance decreases, the resistance of the leads becomes a significant percentage of the total shunt resistance. This has two primary effects on shunt accuracy. First, the effective resistance of the shunt can become dependent on factors such as how long the leads are, how they are bent, how far they are inserted into the board, and how far solder wicks up the lead during assembly. Secondly, the leads are typically made from a material such as copper, which has a much higher tempco than the material from which the resistive element itself is made, resulting in a higher tempco for the shunt overall. Both of these effects are eliminated when a four-terminal shunt is used. A four-terminal shunt has two additional terminals that are Kelvin-connected directly across the resistive element itself; these two terminals are used to monitor the voltage across the resistive element while the other two terminals are used to carry the load current. Because of the Kelvin connection, any voltage drops across the leads carrying the load current should have no impact on the measured voltage. Figure 5 shows an example of two-terminal and four-terminal shunt resistors.
Figure 5 Two-Terminal and Four-Terminal Shunt Resistor Examples[2]
Two-Terminal Four-Terminal Shunt Shunt
PSJ2 PSG4
Several two-terminal and four-terminal SMT shunt resistors suitable for sensing currents in motor drives up to 70 ARMS (71 hp or 53 kW) are shown as examples in Table 1.
Broadcom - 4 - Shunt Resistor Selection for High-Accuracy, Optically Isolated Sigma-Delta Modulator Shunt Resistor Selection Current-Sensing Solution White Paper
Table 1 Example of Two-Terminal and Four-Terminal Shunt Resistors for Motor Drives up to 70ARMS Shunt Maximum RMS Motor Power Range Manufacturer/Shunt Resistor Shunt Resistor Resistance Current 120VAC to 440VAC Part Number Type mΩ A hp kW KOA—CSR series Four-terminal 5 7 1.8 to 6.7 1.4 to 5 Isabellenhütte—BVS series Two-terminal Vishay—WSL4026 series Four-terminal 2 17 4 to 17 3 to 13 Isabellenhütte—BVE series Two-terminal KOA—PSG4 series Four-terminal 1 35 9 to 36 7 to 27 KOA—PSB series Two-terminal Isabellenhütte—BVR series Four-Terminal 0.5 70 19 to 72 14 to 54 KOA—PSJ2 series Two-terminal
A list of manufacturers that supply high-precision current sensing shunt resistors:
Isabellenhuette Isotek KOA Micron Electric Powertron Precision Resistor TT Electronics Vishay
Shunt Resistor Power Derating Curves
As current flows through a shunt resistor, heat generally dissipates to ambient through three paths: conduction, convection, and IR radiation. Heat conducts to ambient from the terminals connected to the shunt resistor and it increases with the size of the terminals. Convection occurs through a natural transfer of heat to ambient and increases with the total surface area of the resistor. The third path is through IR radiation and, similar to convection, increases with the total surface area of the resistor. For SMT shunt resistors, 90% of the heat dissipates through conduction from the shunt resistor terminals mounted on the PCB. Hence, power derating curves measured based on the terminal temperature of shunt resistors is more accurate than ambient temperature near to the shunt resistors based on traditional JIS/IEC derating curve methodology. Implications include the following:
Miniaturization of the SMT shunt resistor as the power rating requirement can be accurately determined Greater factor of safety when deciding design margins for power ratings Reduction in the number of resistors used in the case of paralleling two or more resistors to achieve higher power ratings When considering whether a shunt resistor power rating is sufficient for high-temperature applications, examine the details of the temperature derating curve provided by the shunt resistor manufacturer for greater factors of design safety and margins.
Application Example
Maximum phase current: 70ARMS Shunt resistor value: 0.5 mΩ, ACPL-C799 (±50 mV input) Shunt Resistor Power Rating: 10W (KOA PSJ2) Ambient temperature of the board: 100°C Terminal temperature of the surface mount resistor: 120°C Actual power load: 2.5 W
Broadcom - 5 - Shunt Resistor Selection for High-Accuracy, Optically Isolated Sigma-Delta Modulator PCB Layout and Design Considerations Current-Sensing Solution White Paper
Required margin of safety below rating—according to the designer's internal guidelines: 50%
Figure 6 Temperature-Power Derating Curve of the KOA PSJ2 Shunt Resistor[2]
100
80
60 55
40 50% safety margin % Rated Power Power % Rated 27.5 20
0 –80 –60 –40 –20 0 20 40 60 80 100 120 140 160 180 –65 75 175 Terminal Part Temperature (ºC)
According to Figure 6: Required rated power (2.5W/27.5%) = 9.1W (within the PSJ2 power rating) Overloading condition = 50% of peak current
Power-load surge = (70ARMS x 1.414 x 1.5)2 x 0.5 mΩ = 11.25W (PSJ2 can take 30W at 5 seconds of surge)
PCB Layout and Design Considerations When laying out a PCB for the shunts, a couple of points should be kept in mind.
Bring the Kelvin connections to the shunt together under the body of the shunt and then run them very close to each other to the input of the isolated modulator; this minimizes the loop area of the connection and reduces the possibility of stray magnetic fields from interfering with the measured signal. If the shunt is not located on the same PCB as the isolated modulator circuit, a tightly twisted pair of wires can accomplish the same result. Use multiple layers of the PCB to increase current-carrying capacity. Numerous plated-through vias should surround each non-Kelvin terminal of the shunt to help distribute the current between the layers of the PCB. The PCB should use 2 or 4 oz. copper for the layers, resulting in a current-carrying capacity in excess of 20A. Fairly large current-carrying traces on the PCB can also improve the shunt's power dissipation capability by acting as a heat sink. Liberal use of vias where the load current enters and exits the PCB is also recommended. Figure 7 shows a PCB layout design consideration for a two-terminal shunt resistor.
Broadcom - 6 - Figure 7 PCB Layout Design Consideration of a Two-Terminal Shunt Resistor
2 or 4 oz. Copper Direction of Current Flow
PCB Trace PCB Trace
Vias Kelvin Sense Traces Two-Terminal Shunt Resistor
ACPL-C799
References 1. Avago Technologies, ACPL-C799 Optically Isolated ±50 mV Sigma-Delta Modulator Data Sheet, pub-005830, August 26, 2016. 2. KOA Speer Electronics Inc., Introduction of the Derating Curves Based on the Terminal Part Temperature, Technical Note, April 12, 2014. 3. Avago Technologies, Optoisolation and Optical Sensor Products Selection Guide, AV00-0254EN_042916, April 29, 2016.
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